Fig. 1

Distributed computation of \({\boldsymbol {{\mathcal {D}}}}_{s} \boldsymbol {{y}}\) in a sensor network. Sensor n exchanges messages with its one-hop neighbors for K iterations. After each iteration, the received messages are filtered with weights defined by the graph Laplacian, i.e., zk(n)=(Lzk−1)(n), and are transmitted locally in the network. \(({\boldsymbol {{\mathcal {D}}}}_{s} \boldsymbol {{y}})(n)\) is computed as a linear combination of the messages exchanged during the K iterations